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Theorem exintr 1093
Description: Introduce a conjunct in the scope of an existential quantifier.
Assertion
Ref Expression
exintr |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))
Proof of Theorem exintr
StepHypRef Expression
1 hba1 979 . 2 |- (A.x(ph -> ps) -> A.xA.x(ph -> ps))
2 ancl 294 . . 3 |- ((ph -> ps) -> (ph -> (ph /\ ps)))
32a4s 960 . 2 |- (A.x(ph -> ps) -> (ph -> (ph /\ ps)))
41, 319.22d 1038 1 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))
Colors of variables: wff set class
Syntax hints:   -> wi 3   /\ wa 223  A.wal 950  E.wex 956
This theorem is referenced by:  ceqsex 1809  r19.2z 2318  pwpw0 2439
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-gen 955
This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957
Copyright terms: Public domain